Long‐term and short‐term customer reaction: a two‐stage queueing approach

Abstract

Abstract We analyse a simple, deterministic queueing system with feedback. We model a customer's decision to seek service as a two‐stage process: (1) deciding whether or not to use a facility (become a customer), and (2) deciding the frequency of use (daily, weekly, monthly, etc.). We consider both a constant and a deterministic, time‐dependent usage pattern. We ignore variability, and focus on three forms of feedback: (1) the service rate increases as queue length increases; (2) the frequency with which customers use the service depends on customers' perception of recent waiting times; and (3) the number of customers depends on their perception of long‐term average waiting time. Although highly stylised, this model captures the essential features of many real‐life systems whose average arrival rate varies over time. The main conclusions are that more capacity can make the system less manageable, and a stronger external cycle can be a stabilising factor. The model turns out to be remarkably robust to external disturbances. Copyright © 2006 John Wiley & Sons, Ltd.